A strain sensor or gauge measures a strain on an object due to an external force by converting a mechanical strain into an electronic signal. A strain gauge can include a wire, for example, which, when held under tension, becomes slightly longer and has reduced cross-sectional area. Alternatively, if the wire is under compression, it becomes slightly shorter and its cross-sectional area is increased. In both cases, the change in the cross-sectional area leads to a change in resistance of the strain gauge wire.
A strain gauge is characterized by its strain gauge factor, which is a measure of the sensitivity of the gauge to strain. The strain gauge factor γ is defined as
                    γ        ≡                              1                          R              o                                ⁢                                                    Δ                ⁢                                                                  ⁢                R                                            Δ                ⁢                                                                  ⁢                ɛ                                      .                                              (        1        )            ΔR=R−Ro, where R is the resistance of the gauge wire, when stressed by a strain Δε, and Ro is the unstrained resistance. Usually, if the gauge wire is made of a metal or alloy, the value of γ ranges from 2 to 5. If it is made of polysilicon, the value of |γ| is larger, about 10 to 150. A linearly proportional relationship between the resistance R and the strain can be observed in gauge wires including metals, alloys, and polysilicon. On the other hand, if the wire is made of a ferromagnetic metal or alloy, a maximum value of γ, hereafter denoted as γmax, can be as high as about 150 to 300 either in the positive or the negative Δε region. However, the relationship between the resistance R and the strain Δε becomes non-linear in that R does not vary proportionally with respect to the strain Δε. For a strain sensor having a non-linear relationship of the resistance and the strain, additional circuitry may be required for an accurate determination of the applied strain corresponding to the electrical resistance. Therefore, a linear relationship between the resistance R and the strain Δε is desirable in a strain sensor, in order to obtain an accurate measurement of an applied strain corresponding to a detected resistance value. Since a large maximum strain gauge factor γmax and a linear relationship between the resistance R and the strain Δε are both desirable characteristics of a strain sensor, there is a need for a strain gauge having such characteristics for ultra-sensitive detection of low strain.